A Genealogical Look at Shared Ancestry on the X Chromosome

Close relatives can share large segments of their genome identical by descent (IBD) that can be identified in genome-wide polymorphism data sets. There are a range of methods to use these IBD segments to identify relatives and estimate their relationship. These methods have focused on sharing on the autosomes, as they provide a rich source of information about genealogical relationships. We hope to learn additional information about recent ancestry through shared IBD segments on the X chromosome, but currently lack the theoretical framework to use this information fully. Here, we fill this gap by developing probability distributions for the number and length of X chromosome segments shared IBD between an individual and an ancestor k generations back, as well as between half- and full-cousin relationships. Due to the inheritance pattern of the X and the fact that X homologous recombination occurs only in females (outside of the pseudoautosomal regions), the number of females along a genealogical lineage is a key quantity for understanding the number and length of the IBD segments shared among relatives. When inferring relationships among individuals, the number of female ancestors along a genealogical lineage will often be unknown. Therefore, our IBD segment length and number distributions marginalize over this unknown number of recombinational meioses through a distribution of recombinational meioses we derive. By using Bayes' theorem to invert these distributions, we can estimate the number of female ancestors between two relatives, giving us details about the genealogical relations between individuals not possible with autosomal data alone.